KVS MATHEMATICS QUIZ 4 (ALGEBRA)

If $x^2+y^2+z^2=xy+yz+zx$, then value of, $\frac{7x^7+9y^5+11z^3}{4x^3{y}^2+3y^3{z}^2+2z^3{x}^2}$ is:

The value of

$\frac{(2.9{)}^3+(8.7{)}^3}{(2.9{)}^2-2.9\times 8.7+(8.7{)}^2}$ is:

What is the value of the expression?

$\frac{(a-b{)}^3+(b-c{)}^3+(c-a{)}^3}{3(a-b)(b-c)(c-a)}=\text{ ? }$

Which of the following option is correct.

$a^3+b^3=(a-b)(a^2+b^2+ab)$

$a^3+b^3=(a+b)(a^2-b^2-ab)$

$a^3-b^3=(a-b)(a^2+b^2-ab)$

$a^3+b^3=(a+b)(a^2+b^2-ab)$

If $(a+b+c)=0$ and $(abc)=12$, then what is the value of $(a^3+b^3+c^3)?$

If $(3+2\sqrt{2})a=(3-2\sqrt{2})b$, then $\frac{1}{a}+\frac{1}{b}$ is:

If $a^2+b^2=40$ and $ab=10$ then the value of $(\sqrt{a-b}{)}^2$ is ?

If $x=5-\frac{1}{x}$ then what is value of $x^2+\frac{1}{x^2}$.

Solve : $a^2-b^2=?$